Fuzzy Resolution Research Articles

An analytical framework for knowledge-based tuning of servo controllers

This paper investigates the knowledge-based tuner of a two-level control structure in which a crisp servo controller that occupies the lower level is tuned by a fuzzy logic tuner at the upper level. First the knowledge-based tuner is expressed in the conventional fuzzy-logic formulation of a linguistic rule base to which the compositional rule of inference may be applied. Next the concepts of rule dissociation and fuzzy resolution are introduced, and resolution relationships are defined to build an analytical framework for the tuning problem. Stability of the overall control system is discussed in terms of the stability of the original system. Computational requirements for the tuning system are analyzed to show that a substantial reduction in computational effort can be achieved through this analytical framework. An example of tuning a PID controller of a nonminimum-phase plant with transport delay is presented to illustrate the application of the concepts that are developed in the paper.

Reasoning under uncertainty in fuzzy operator logic

The authors present an approach to fuzzy logic and reasoning using the resolution principle based on a novel operator, the fuzzy operator. After presenting the fuzzy resolution principle, a general methodology for reasoning under uncertainty, based on resolution in this fuzzy logic, is discussed. The calculus presented is referred to as fuzzy operator logic or FOL. Some simple examples illustrating the reasoning process using FOL are included. >

A two-level servo structure with knowledge-based tuning

This paper presents a two-level structure for servo controllers. The lower level is occupied by a conventional servo loop of the proportional-integral-derivative type. The upper level consists of a knowledge-based tuner for the servo parameters. Expert knowledge expressed in the form of linguistic fuzzy rules represents the knowledge base for servo tuning. These rules, along with membership functions for condition and action variables, are processed through fuzzy logic to obtain a multi-dimensional membership function for the knowledge. Tuning inferences are made from the response of the servo loop by applying the compositional rule of inference to the knowledge base. This paper presents a general theory for the development of a knowledge-based tuner. Specifically, the concepts of fuzzy resolution and rule dissociation are introduced. A parallelism between conventional parameter-adaptive control and fuzzy tuning control is pointed out. Through rule dissociation to an elementary level, the fuzzy resolution is arbitrarily improved. By introducing a monotonicity assumption, an analytical framework is established. It is shown that in this framework, fuzzy tuning may be expressed as an algebraic scheme, and consequently the dynamic characteristics such as stability of the overall tuning system may be established purely from the dynamics of the original system. A numerical example is presented to illustrate the basic scheme of fuzzy tuning.

Fundamentals of Fuzzy Prolog

In this paper, a Fuzzy Prolog is introduced that is based on the fuzzy resolution principle. There are three levels of concern: (1) the fuzzy truth values of predicates that depend on several values of individual variables, (2) the weights of rules that depend on several fuzzy truth values of premise and conclusion, and (3) the confidence of resolvent that depends on the fuzzy resolution principle. With these three levels, we introduce fuzziness into the resolution principle and unification and cause fuzzy logical inference to be significant in Fuzzy Prolog when the values of all variables are taken in the closed interval [0, 1].